Multi-mode resource-constrained project scheduling problem with multiple shifts and dynamic energy prices

Considering the characteristics of time-of-use tariffs and multi-shifts in real-life project execution scenarios, we present a multi-mode resource-constrained project scheduling problem with multi-shift and time-of-use tariffs (MRCPSP-MS-TOU). The MRCPSP-MS-TOU is a bi-objective scheduling problem that aims to simultaneously minimise both project duration and energy costs. In this problem, renewable resources are the critical equipment that consumes the most energy and can work continuously for multiple shifts. Activities that require critical equipment with high energy consumption are given priority for shifts with lower electricity prices under time-of-use tariffs. We construct a mixed integer linear programming model for the MRCPSP-MS-TOU. For small-scale projects, the ε-constraint method is implemented to solve the MRCPSP-MS-TOU using the Gurobi optimiser. For large-scale projects, this paper develops meta-heuristic algorithms in the framework of the two non-dominated sorting genetic algorithm versions. The MRCPSP-MS-TOU enables manufacturers and the construction industry to schedule projects using time-of-use tariffs and multi-shifts in a more efficient manner since it can control the intensity of energy consumption, reduce project costs, make full use of energy-intensive equipment, and effectively reduce order delivery time.